Helicopter Rotor/Fuselage Coupling Aeroelastic Response And Bifurcation Research

The rotor/fuselage coupling system aeroelastic response, stability and bifurcation problem is one of the research hotspots and challenges in helicopter dynamics field. In this thesis, nonlinear dynamics theory and qualitative method, mainly including newly developed Chebyshev series theory and normal form method suggested by Yu, are adopted. Then helicopter system aeroelastic response, stability and local bifurcation are investigated profoundly.Chebyshev series method is proposed to calculate the steady-state periodic solution of nonlinear vibration system. Taking Duffing equation as an example, the system residual obtained by Chebyshev series method is compared with harmonic balance method residual. It is proved that Chebyshev series method has higher precision, meanwhile, Chebyshev series solution is more favorable for solving Floquet transition matrix(FTM) rapidly and accurately, so as to effectively reduce the analysis error.According to moderate deflection beam theory, quasi-steady aerodynamic model and Hamilton variational principle, helicopter rotor and rotor/fuselage coupling system dynamics models are estabilished. Then steady-state periodic response of the above systems are solved by Chebyshev series method. Compared the results with the ones obtained by harmonic balance method, Runge-Kutta method and time finite element method, the correctness of Chebyshev series methods are verified, and the stability of periodic response is analyzed by computing FTM.A normal form method proposed by Yu is firstly introduced to the blade/absorber system combination resonance analysis. Two kinds of critical condition for the averaged equations are studied, which are characterized by a pair of purely imaginary eigenvalues as well as a double zero eigenvalues. The bifurcation solution, bifurcation path, and transition curves of the model are obtained respectively, and initial equilibrium stability region is given. For each case, the numerical results obtained by Runge-Kutta method coincide with the predictive analysis ones.A modified helicopter rotor/absorber dynamic equation is established. The stability and local bifurcation characteristics near combination resonance are predicted via normal form method proposed by Yu. The theoretical prediction results are in good agreement with that of Runge-Kutta numerical method. Compare the bifurcation points with the simplified model, it is more accurately to decide the bifurcation character via the modified model.Considering the precone effect and without the small angle assumption, a helicopter fuselage/rotor/absorber motion model is established using Lagrange equation. System stability and local bifurcation characteristics near subharmonic resonance is analyzed, then transition curves, stability region and bifurcation path are obtained. The correctness of the above theoretical prediction is verified by Runge-Kutta method.The normal form method proposed by Yu is firstly applied to study the bifurcation phenomena of helicopter ground resonance. Then bifurcation point, bifurcation path and stability region are given. It is verified that theoretical prediction and Runge-Kutta numerical simulation results are in good agreement.